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Syllabus Of Investigators Examination

Syllabus of Investigators Examination conducted by SSC is give as under:

Statistics

Probability, Probability Distributions: Binomial, Poisson, Normal, Exponential. Compilation, classification, tabulation of statistical data, Graphical presentation of data. Measures of central tendency, measures of dispersion, measures of association and contingency, scatter diagram, correlation coefficient, rank correlation efficient and linear regression analysis (for two or more variables) excluding partial correlation coefficients. Concept of Population, random sample, parameters, statistics, sampling distribution of x, properties of estimators and estimation of confidence intervals. Principles of sampling, simple random sampling, stratified sampling, systematic sampling, etc. Sampling and Non-sampling errors, type-I and type-II errors. Concepts of Hypothesis: Null and alternate. Testing of hypothesis for large samples as well as small samples including Chi-square tests (Z,t,F,X tests). Index Numbers, Time series analysis-components of variation and their estimation.

Economics

(A) General Economics

(B) Indian Economics & General Statistics:

Mathematics

Algebra:

Algebra of sets, relations and functions, Inverse of a function, equivalence relation. The system of complex numbers, De Moivere's Theorem and its simple applications. Relation between roots and coefficients of a polynomial equation - Evaluation of symmetric function of roots of cubic and biquadratic equation.

Algebra of Matrices:

Determinants, Simple properties of determinants, multiplication of determinants of orders two and three. Singular and non-singular matrices. Inverse of a matrix, Rank of a matrix and application of matrices to the solution of linear equations (in three unknowns). Convergence of sequences, and series, tests of convergence of series with positive terms, Ration, Root and Gauss tests.

Analytical Geometry:

Straight lines, Circles, system of circles, parabola, ellipse and hyperbola in standard form and their elementary properties. Classification of curves second degree. Differential Equation: First order differential equation. Solution of Second and higher order linear differential equations with constant coefficients and simple applications.

Differential and Integral Calculus:

Limit, continuity and differentiability of functions, successive differentiation, derivatives of standard functions, Rolle's and Mean-value Theorems, Maclaurins and Taylor's series ( without proof) and their applications, maxim and minima of functions of one variables. Tangents and normals, curvature, Partial differentiation, Euler's theorem for omogeneous function, Tracing of curves. Standard methods of integration. Riemann's definition of definite integral, fundamental theorem of integral calculus, quadrate, rectification, volumes and surface area of solids of revolution.

Statistics:

Frequency distributions, Measures of central tendency, measures of dispersion, Skewness and kurtosis. Random variables and distribution function. Discrete distributions. Binomial and Poisson distribution. continuous distributions. Rectangular, Normal and exponential distributions. Principles of least squares, correlation and regression. Random Sampling, random numbers. Sampling of attributes. Large Sample tests for mean and proportion. Tests of significance, based on t, F and Chi square distributions.

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